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Abstract Gallium-based liquid metals (LM) have surface tension an order of magnitude higher than water and break up into micro-droplets when mixed with other liquids. In contrast, silicone oil readily mixes into LM foams to create oil-in-LM emulsions with oil inclusions. Previously, the LM was foamed through rapid mixing in air for an extended duration (over 2 hours). This process first results in the internalization of oxide flakes that form at the air-liquid interface. Once a critical fraction of these randomly shaped solid flakes is reached, air bubbles internalize into the LM to create foams that can internalize secondary liquids. Here, we introduce an alternative oil-in-LM emulsion fabrication method that relies on the prior addition of SiO2 micro-particles into the LM before mixing it with the silicone oil. This particle-assisted emulsion formation process provides a higher control over the composition of the LM-particle mixture before oil addition, which we employ to systematically study the impact of particle characteristics and content on the emulsions' composition and properties. We demonstrate that the solid particle size (0.8 µm to 5 µm) and volume fraction (1% to 10%) have a negligible impact on the internalization of the oil inclusions. The inclusions are mostly spherical with diameters of 20 to 100 µm diameter and are internalized by forming new, rather than filling old, geometrical features. We also study the impact of the particle characteristics on the two key properties related to the functional application of the LM emulsions in the thermal management of microelectronics. In particular, we measure the impact of particles and silicone oil on the emulsion's thermal conductivity and its ability to prevent deleterious gallium-induced corrosion and embrittlement of contacting metal substrates.
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Self-similarity in particle accumulation on the advancing meniscus
When a mixture of viscous oil and non-colloidal particles displaces air between two parallel plates, the shear-induced migration of particles leads to the gradual accumulation of particles on the advancing oil–air interface. This particle accumulation results in the fingering of an otherwise stable fluid–fluid interface. While previous works have focused on the resultant instability, one unexplored yet striking feature of the experiments is the self-similarity in the concentration profile of the accumulating particles. In this paper, we rationalise this self-similar behaviour by deriving a depth-averaged particle transport equation based on the suspension balance model, following the theoretical framework of Ramachandran ( J. Fluid Mech. , vol. 734, 2013, pp. 219–252). The solutions to the particle transport equation are shown to be self-similar with slight deviations, and in excellent agreement with experimental observations. Our results demonstrate that the combination of the shear-induced migration, the advancing fluid–fluid interface and Taylor dispersion yield the self-similar and gradual accumulation of particles.
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- PAR ID:
- 10319751
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 925
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.647
